New questions arose yesterday over how much money the Department of Education saved when it reorganized under Mayor Bloomberg’s Children First program, one of the key planks of the mayor’s re-election campaign.

For months, Schools Chancellor Joel Klein has been crowing about $250 million he said he had whittled out of the department’s bloated budget. That money, he testified before various committees of the City Council, was redirected to the city’s classrooms, where it belongs. Now a new comptroller’s report suggests that the savings were much less than what Mr. Klein had said they were – $140 million – and says the department is hard-pressed to show where, precisely, the money has gone.

“Creative bookkeeping, that’s what I am alleging,” the comptroller, William Thompson Jr., told The New York Sun in an interview. “I am not saying this is fraud, but I do think that they played with the numbers to make things look better than they are. We’ve been unable to independently verify that the DOE increased its investment in the classroom by $250 million between fiscal 2002 and fiscal 2004.”

Mr. Thompson’s staff found that of the $140 million in achieved savings, only $4 million could be attributed directly to cost-cutting at department headquarters.

Further, the analysts said there was no evidence to show that the savings ended up in new spending in classrooms, as the department has assured parents.

What is more, by the comptroller’s reckoning, between fiscal years 2002 and 2004, the head count at the department’s central offices increased by 94 people instead of declining by 700 as the department has said.

“Ever since Chancellor Klein began to flesh out his vision for Children First, I have asked how much money it would save, how much money would be driven into the classroom, and who would have the discretion to spend it,” the chairwoman of the council’s Committee on Education, Eva Moskowitz, said. “I haven’t gotten a straight answer yet. I agree with the comptroller, this amounts to a shell game.”

The comptroller’s office had alerted Mr. Klein early last year to the tracking problems in the department, and, according to a letter obtained by the Sun, Mr. Thompson sent a letter to the chancellor in July to discuss how the department was keeping its books.

“I am writing to express my concern that the DOE fiscal reporting practices have become markedly less transparent since the Department’s restructuring,” the July letter from Mr. Thompson began. “The expense data the DOE now provides to my office are also far less transparent than in previous fiscal years. DOE has misapplied certain units of appropriation to report expenditures, commencing with FY 2004, in a way that makes it difficult, if not impossible, to track its use of public funds.”

It is about those “units of appropriation” that the two sides – Mr. Thompson and the department – are arguing. A unit of appropriation is a measure of spending. It is easiest to think of it as a box in which all the receipts for spending on, say, pencils are placed. If receipts for other things are put in that box – spending on erasers or pens – then it is difficult to track what is spent. Mr. Thompson has objected to the big, amorphous categories the department has used to catalogue spending.

“If you throw other things into that unit of appropriation, or code, you can’t tell how much you spent on pencils,” Mr. Thompson, a former president of the Board of Education, explained. “Instead, their budget is like a big messy drawer. Everything is mixed together. That’s the problem we’re having. We’ve been meeting every six weeks for months now to try to reconstruct their budget, and we still can’t figure it out.”

The deputy chancellor of finance, Kathleen Grimm, told reporters yesterday that the department stood by its numbers. “We have had very dramatic changes at the department, and as we do the comparison of the costs in fiscal 2002 and 2004, we’re not really comparing apples to apples,” she said.

There was $83 million in savings in the department’s central administration offices, she said, a figure that the comptroller’s office and department officials largely agree upon. All told, about 700 jobs were consolidated to whittle down the workforce, Ms. Grimm said, a number that Mr. Thompson disputes.

The department went $156 million over budget last year, saying it had unanticipated costs for special education as well as administrative costs associated with making the department’s budget dovetail better with the city’s general budget. Mr. Thompson said he can’t track those expenditures in anything the department has provided to his office.

As far as redirecting money to the classrooms, Ms. Grimm said the department spent $145 million on coaches for students, another $38 million on parent coordinators, and $62 million on new curriculum.

Mr. Bloomberg, who has asked voters to judge his mayoralty on the success or failure of his education reforms, told reporters yesterday: “All the money is fungible. I think the only difference of opinion is how you categorize some things. I think Billy Thompson is a very good comptroller of the city of New York, but that doesn’t mean I have to agree with all of his views.”

Unfortunately for Mr. Bloomberg, the comptroller’s findings brought his critics to the fore at a time when he is trying to make a case for four more years. A Baruch College professor of political science, Douglas Muzzio, said yesterday was only the beginning.

“Clearly, Thompson lobbed a grenade at the campaign,” he said.

Public Advocate Betsy Gotbaum said yesterday’s report confirmed everyone’s worst fears about the Department of Education. “They didn’t save $250 million, just like they didn’t fix the problems with special education, didn’t raise test scores, didn’t adequately deal with unruly and disruptive students, and didn’t address the overcrowding problems in our schools,” she said.

The Democratic front-runner in the race to unseat the mayor, Fernando Ferrer, said, “Bloomberg moved the address of the Department of Education from 110 Livingston Street to Tweed Courthouse, but the problems of accountability and transparency have gotten worse.”

Another Democratic contender, Gifford Miller, weighed in, too. “The comptroller’s finding show a disturbing lack of accountability at the Department of Education,” the council speaker said. “We need honest transparency, not deceiving inflated numbers. There has to be oversight that tells parents exactly where and how much money is being spent.”